It is known in the art that the velocity of a sound wave in a material depends on the mechanical properties of the material. This phenomena is described, for example, by C. H. Hastings and S. W. Carter in an article entitled "Inspection, Processing and Manufacturing Control of Metal by Ultrasonic Methods," Symposium on Ultrasonic Testing, 52nd Annual Meeting of the American Society for Testing Materials, Jun. 28, 1949, pp. 16-47.
U.S. Pat. Nos. 3,720,098, 3,228,232, 3,288,241, 3,372,163, 3,127,950, 3,512,400, 4,640,132, 4,597,292 and 4,752,917 describe the state of the art of non-destructive testing using ultrasound.
A sound wave which reaches a semi-infinite solid at an angle will typically propagate through and along the solid as three waves, namely, longitudinal, transverse and surface waves, wherein each wave has a different velocity. As described by Hastings and Carter, the velocities of the three waves are: ##EQU1##
where V.sub.L, V.sub.T, and V.sub.S are, respectively, the velocities of the longitudinal, transverse and Raleigh surface waves, and E, .sigma. and rho are, respectively, the Young's Modulus, the Poisson's ratio of lateral contraction to longitudinal extension and the mass density of the material. Equation (3b) is an empirical relationship as defined on page 326 of Wave Motion in Elastic Solids, by Karl F. Graff, published by the Clarendon Press, Oxford England in 1975.
In ultrasonic measurement of the condition of bone, typically only the velocity of the longitudinal wave is used. In an article entitled, "Osteoporotic Bone Fragility: Detection by Ultrasound Transmission Velocity," R. P. Heaney et al., JAMA, Vol. 261, No. 20, May 26, 1989, pp. 2986-2990, the Young's Modulus of bone, E, is given empirically as: EQU E=K(rho).sup.2 (4a)
The velocity of the longitudinal sound wave in the bone is given as: ##EQU2##
where K is a constant which incorporates a number of factors, such as spatial orientation of the bone structures, inherent properties of the bone material and fatigue damage. Thus, the velocity of a longitudinal wave is a function of the mass density and can be used as an indicator of the quality of bone.
The following articles also discuss ultrasonic measurement of bone condition both in vivo and in vitro:
"Measurement of the Velocity of Ultrasound in Human Cortical Bone In Vivo," M. A. Greenfield, et al., Radiology Vol 138, March 1981, pp. 701-710; and
"Combined 2.25 MHz ultrasound velocity and bone mineral density measurements in the equine metacarpus and their in vivo applications," R N. McCartney and L. B. Jeffcott, Medical and Biological Engineering and Computation, Vol. 25, 1987, Nov. 1877, pp. 620-626.
In order to perform in vivo ultrasonic measurements of the mechanical properties of bone, it is necessary to transmit an ultrasonic wave through the soft tissue surrounding the bone. Unfortunately, the thickness of the soft tissue varies along the length of the bone. This thickness variation can affect the accuracy of the ultrasound propagation time measurement through the bone. In the abovementioned articles, the thickness of the soft tissue is either ignored or an attempt is made to cancel the effects of the soft tissue. In the articles describing in vitro experiments, the soft tissue is removed from the bone.
Russian patents 1,420,383, 1,308,319, 1,175,435, 1,324,479, 1,159,556 and 1,172,534 and U.S. Pat. Nos. 4,926,870, 4,361,154, 4,774,959, 4,421,119, 4,941,474, 3,847,141, 4,913,157 and 4,930,511 describe various systems for measuring the strength of bone based on the velocity V.sub.L. These systems typically have one ultrasonic signal transmitter and at least one ultrasonic signal receiver.
Russian patents 1,420,383, 1,308,319 and 1,175,435 attempt to solve the problem of the unknown thickness of the soft tissue by assuming values for the thickness of the soft tissue in the area of the measurement or by assuming that the thickness variation is small over the distance between two ultrasonic signal receivers.
Russian patent 1,342,279 utilizes two receivers and a single transmitter and calculates an average group speed through the bone based on the known distance between the two receivers.
Russian patent 1,159,556 defines zones of a bone and the condition of a bone is determined by the difference between the maximum and minimum amplitude of the ultrasound signals measured, different zones having different velocities. It appears that this measurement is performed on an excised bone.
Russian patent 1,172,534 describes a system which compares the ultrasound signal of a healthy bone with that of an unhealthy bone and from the comparison, produces a diagnosis of the extent of disease in the unhealthy bone.
U.S. Pat. Nos. 4,926,870, 4,421,119 and 3,847,141 describe systems which places a receiver and a transmitter on opposite sides of a bone. U.S. Pat. No. 4,926,870 also compares the resultant signal with a canonical waveform, thereby to classify the health of the bone.
U.S. Pat. Nos. 4,913,157, 4,774,959 and 4,941,474 describe systems which transmit an ultrasonic signal with a spectrum of frequencies.
U.S. Pat. No. 4,930,511 describes a system which is placed around a standard inanimate homogeneous material of known acoustic properties before it is placed around a bone.
U.S. Pat. No. 5,143,072, the disclosure of which is incorporated herein by reference, describes a method of overcoming the effects of the unknown thickness of the intervening soft tissue. FIG. 1A, which illustrates the method of this patent, shows an ultrasonic transmitter 2 and two ultrasonic receivers 4 and 6, all of which are collinear. Transmitter 2 transmits an ultrasonic wave through soft tissue 22 towards a bone 18. The first signal received at receiver 4 passes through the fastest path. This path includes a first soft-tissue path portion 8, a bone surface portion 10 and a second soft-tissue path portion 14. An angle 23 between path 8 and path 10 is determined by the ratio between the acoustic velocity in bone 18 and the acoustic velocity in soft-tissue 22. The first signal received by receiver 6 passes through first soft-tissue path portion 8, bone surface portion 10, an additional bone path portion 12 and a third soft-tissue path portion 16. The propagation times for the first received signals at receivers 4 and 6 are measured. If receivers 4 and 6 are aligned so that path 14 and path 16 are of the same length, subtracting the two signal propagation times yields the signal propagation time in bone portion 12. Since bone portion 12 has the same length as the distance between receiver 4 and receiver 6, the acoustic velocity in bone portion 12 can be determined.
FIG. 1B shows a method disclosed by the '072 patent for assuring that path 16 and path 14 have the same length Receivers 4 and 6 are also transmitters, and they are used to measure the wave propagation times along paths 30 (and 32) between receivers 4 (and 6) and bone 18. In an additional embodiment disclosed, transmitter 2 and receivers 4 and 6 are mounted on a rocker, which compresses soft tissue 22 when it rocks, such that when the propagation times along paths 30 and 32 are found to be equal, acoustic bone velocity is determined.
However, even this method has several serious shortcomings. First, soft tissue velocity is not a constant, rather, it varies with the type of soft tissue. Since the propagation paths 30 and 32 are not the same as paths 14 and 16, the propagation times along paths 14 and 16 may be unequal and the calculated acoustic bone velocity is not correct, even if the propagation times along paths 30 and 32 are equal. Second, the above described method requires a relatively long portion of flat bone. Thus, only a small number of bones can be tested, using this method, such as the tibia In addition, since high frequency ultrasonic waves are very lossy, it is not practical to use them for this method. Third, the spatial resolution of this method is relatively low, approximately 2-5 cm.